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Ohm’s Law
John Denker

Ohm’s law is commonly written

 V = IR
(1)

where it is understood that V is the voltage drop across the resistor. That is, if we travel along the circuit in the direction of positive conventional current I, then the voltage on the downstream end of the resistor is lower than the voltage on the upstream end.

Note that if I move from a lower elevation to a higher elevation, the Δh is positive, according to the long-established conventional meaning of “Δ”.

Therefore it is not entirely logical to write Ohm’s law as

 ☠       ΔV = IR       ☠
(2)

even though this is extremely common. Either there is a minus sign missing from equation 2, or they are using an exceedingly misleading idosyncratic definition of “Δ”, or they are going around the circuit backwards, contrary to the direction of positive conventional current.

It is smarter to write the voltage drop in the form

 Vdrop = IR
(3)

or even more explicitly as

 V1 − V2 = IR
(4)

where V1 is the upstream voltage and V2 is the downstream voltage.

Note that sticking absolute value bars into Ohm’s law is not an acceptable way to fix the problem. That’s because the equations with absolute value bars in them represent relationships that are wildly different from Ohm’s law. This should be obvious from the following figures.

Figure 1: V=IR

Ohm’s Law

 Figure 2: V=|IR| Figure 3: |V|=IR Not Ohm’s Law Not Ohm’s Law

Figure 4: |V|=|IR|

Not Ohm’s Law

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